Write the equation for the parabola shown in factored form. Remember to include the stretch factor.

(Determine an equation for the parabola in factored form. Don't forget the stretch factor)

Now, factor the trinomial 4 x^2+13 x-12. To do this, use the factors of as the first terms of two binomials and factors of -12 as the last terms of the binomials. The factorization whose inner and outer products combine to .

 

So, the equation, , can be written in factored form as 5(x+4)(4 x-3)=0. Remember that, 5 0. So, to solve further, simplify (x+4)(4 x-3)=0.

Next, to solve further, use the zero product property. For real numbers a and b, if the product a b=0, then either a=0 or b=0.

Because 5 0, apply the zero product property to (x+4)(4 x-3)=0.

 

(x+4)(4 x-3)=0 

x+4=0   or  4 x-3=0 

 

x = -4  or  x=-4, Solve the linear equations. 

 

The solutions to